Semi-local scaling and turbulence modulation in variable property turbulent channel flows

Abstract

We theoretically and numerically investigate the effect of temperature dependent density and viscosity on turbulence in channel flows. First, a mathematical framework is developed to support the validity of the semi-local scaling as proposed based on heuristic arguments by Huang, Coleman, and Bradshaw ["Compressible turbulent channel flows: DNS results and modelling," J. Fluid Mech. 305, 185-218 (1995)]. Second, direct numerical simulations (DNS) of turbulent channel flows with different constitutive relations for density and viscosity are performed to assess and validate the semi-local scaling for turbulent statistics. The DNS database is obtained by solving the low-Mach number approximation of the Navier-Stokes equation. Finally, we quantify the modulation of turbulence due to changes in fluid properties. In the simulations, the fluid is internally heated and the temperature at both channel walls is fixed, such that the friction Reynolds number based on wall quantities is Re τ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity µ, but constant semi-local Reynolds number Re * τ ≡  (ρ/ρ w )/(µ/µ w )Re τ (where bar and subscript w, denote Reynolds averaging and averaged wall quantity, respectively), across the whole channel height, the turbulent statistics exhibit quasi-similarity with constant property turbulent flows. For cases where Re * τRe τ across the channel, we found that quasi-similarity is maintained for cases with similar Re * τ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Re * τ towards the channel center (Re * τ < Re τ ), we show that the anisotropy increases and the pre-multiplied stream-wise spectra reveal that this increase is associated with strengthening of the large scale streaks in the buffer layer. The opposite effect is observed when Re * τ increases towards the channel center. The present results provide an effective framework for categorizing turbulence modulation in wall-bounded flows with variable property effects, and can be applied to any Newtonian fluid that is heated or cooled. C 2015 AIP Publishing LLC. [http://dx

Scalar statistics in variable property turbulent channel flows

“…Similar observations can be made for cases LL and VλSPr LL , which have quasisimilar Pr but different Re τ . Although not shown here, it should be noted that, similar to statistics of velocity fluctuations discussed by Patel et al [15], it was found that ρθ 2 ≈ ρθ 2 , but ρ 1.5 θ 3 = ρ 1.5 θ 3 . This highlights the importance of including density fluctuations in third-order moments, because of the functional relation between density and temperature, which causes a preferential concentration of a high-density fluid in a low-temperature streak, and vice versa.…”

“…As shown in previous works [11,12,15,16,23,24,30], the semilocal wall coordinate y is effective in accommodating changes in viscous scales due to variable properties, thus providing a meaningful representation for the turbulent velocity statistics. Therefore, all wall-normal profiles are plotted as a function of y in the present work.…”

“…In our previous work [15], we provided a theoretical framework for the semilocal scaling that has been proposed based on heuristic arguments by Huang et al [23]. In contrast to the conventional scaling with wall values, the semilocal scaling uses the wall-shear stress τ w and the mean local properties to define the characteristic friction velocity and viscous length scale as u τ = √ τ w /ρ and δ v = μ/ρu τ , respectively (bar denotes Reynolds averaging).…”

“…In all such cases, the effects of thermophysical property variations can be strong enough to modulate turbulence and the traditional approach of treating temperature as a passive scalar no longer holds. Although turbulence modulation in a turbulent channel flow due to variable thermophysical properties has been investigated in great detail in high-Mach-number flows [9][10][11][12] and in low-Mach-number flows [13][14][15][16], the effect of property variations on scalar transport is not well understood. Lee et al [17] studied the influence of wall heating on turbulent thermal boundary layers with variable viscosity and observed variations in mean scalar, scalar fluctuation, and scalar flux, relative to a reference isothermal flow.…”

DNS of turbulent flows of dense gases

“…This mixed scaling (recently discussed in [22]) has proven to give quite satisfactory results in collapsing first-and second-order moments [21] obtained from a wide range of M Bw . We recall that in case of an incompressible flow, Re τ * = Re τ .…”